Place the sea bass in a glass bowl. Mix together the lime juice and the coconut milk in a jug. Pour over the fish, then cover with clingfilm and leave to marinate in the refrigerator for 3 hours until the fish turns opaque and white.
Drain the fish, reserving the liquid. Toss together the fish, oil, tomatoes and chilli in a serving bowl. Stir through 2 tablespoons of the reserved fish liquid, then scatter over the coriander and coconut curls. Serve immediately.